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Abstract：
The National Mental Health Survey of India (NMHS) was a ground-breaking nationwide study that harnessed a uniform, standardized methodology blending quantitative and qualitative approaches. Covering data from 12 states across diverse regions, its mission was to gauge the prevalence of psychiatric disorders, bridge treatment gaps, explore service utilization, and gauge the socioeconomic repercussions of these conditions. This initiative provided pivotal insights into the intricate landscape of mental health in India. One of the analyses planned for NMHS data was to undertake a logistic regression analysis with an aim to unravel how various sociodemographic factors influence the presence or absence of specific psychiatric disorders. Within this pursuit, two substantial challenges loomed. The first pertained to data separation, a complication that could perturb parameter estimation. The second challenge stemmed from the existence of disorders with lower prevalence rates, which resulted in datasets of limited density, potentially undermining the statistical reliability of our analysis. In response to these data-driven hurdles, NMHS recognized the critical necessity for an alternative to conventional logistic regression, one that could adeptly navigate these complexities, ensuring robust and dependable insights from the collected data. Traditional logistic regression, a widely prevalent method for modeling binary outcomes, has its limitations, especially when faced with limited datasets and rare outcomes. Here, the problem of \"complete separation\" can lead to convergence failure in traditional logistic regression estimations, a conundrum frequently encountered when handling binary variables. Firth\'s penalized logistic regression emerges as a potent solution to these challenges, effectively mitigating analytical biases rooted in small sample sizes, rare events, and complete separation. This article endeavors to illuminate the superior efficacy of Firth\'s method in managing small datasets within scientific research and advocates for its more widespread application. We provide a succinct introduction to Firth\'s method, emphasizing its distinct advantages over alternative analytical approaches and underscoring its application to data from the NMHS 2015-2016, particularly for disorders with lower prevalence.
摘要：
印度国家心理健康调查（NMHS）是一项开创性的全国性研究，利用制服，混合定量和定性方法的标准化方法。涵盖来自不同地区的12个州的数据，它的任务是评估精神疾病的患病率，桥梁处理间隙,探索服务利用，并评估这些条件的社会经济影响。这一举措为印度心理健康的复杂局面提供了关键的见解。计划对NMHS数据进行的分析之一是进行逻辑回归分析，目的是弄清各种社会人口统计学因素如何影响特定精神疾病的存在与否。在这种追求中，两个重大挑战迫在眉睫。第一个涉及数据分离，可能扰乱参数估计的复杂性。第二个挑战源于患病率较低的疾病的存在，这导致了有限密度的数据集，可能会破坏我们分析的统计可靠性。为了应对这些数据驱动的障碍，NMHS认识到替代传统逻辑回归的关键必要性，一个可以巧妙地驾驭这些复杂性的人，确保从收集的数据中获得可靠可靠的见解。传统逻辑回归，一种广泛流行的二元结果建模方法，有其局限性，特别是当面对有限的数据集和罕见的结果时。这里,“完全分离”的问题会导致传统逻辑回归估计的收敛失败，处理二进制变量时经常遇到的难题。Firth的惩罚逻辑回归成为应对这些挑战的有效解决方案，有效缓解源于小样本量的分析偏见，罕见事件,完全分离。本文试图阐明Firth方法在科学研究中管理小数据集方面的卓越功效，并倡导其更广泛的应用。我们简要介绍了Firth\的方法，强调其相对于替代分析方法的独特优势，并强调其在NMHS2015-2016年数据中的应用，特别是对于患病率较低的疾病。
